相关论文: A semi-symmetric metric connection, perfect fluid …

Building upon previous works characterizing GRW space-times using concircular and torse-forming vectors, this paper investigates a Lorentzian manifold equipped with a concircularly semi-symmetric metric connection. We demonstrate that such…

In this article, we characterize a Lorentzian manifold $\mathcal{M}$ with a semi-symmetric metric connection. At first, we consider a semi-symmetric metric connection whose curvature tensor vanishes and establish that if the associated…

In this paper, we define the semi-symmetric metric connection on super Riemannian manifolds. We compute the semi-symmetric metric connection and its curvature tensor and its Ricci tensor on super warped product spaces. We introduce two kind…

In the present paper we introduce a semi-quasi-Einstein manifold from a semi symmetric metric connection. Among others, the popular Schwarzschild and Kottler spacetimes are shown to possess this structure. Certain curvature conditions are…

In this paper we introduce the concept of $(\varepsilon)$-almost paracontact manifolds, and in particular, of $(\varepsilon)$-para Sasakian manifolds. Several examples are presented. Some typical identities for curvature tensor and Ricci…

In the present paper we discuss about a set of geometric properties and physical applications of a mixed quasi-Einstein spacetime$[M(QE)_{4}]$, which is a special type of nearly quasi-Einstein spacetime$[N(QE)_{4}]$. Firstly we consider a…

Spacetime is a 4-dimensional connected Lorentzian manifold. In this paper, we extend the Levi-Civita connection in the definition of spacetime to the semi-symmetric non-metric connection and conclude geometric structures admitted by the…

In this paper, we define a semi-symmetric non-metric connection on super Riemannian manifolds. And we compute the curvature tensor and the Ricci tensor of a semi-symmetric non-metric connection on super warped product spaces. Next, we…

A.Einstein considered a linear connection $\nabla$ with torsion $T$ on a smooth manifold equipped with a nonsymmetric (0,2)-tensor $G=g+F$, where $g$ is a pseudo-Riemannian metric associated with gravity, and $F\ne0$ is a skew-symmetric…

We complete the intrinsic characterization of spherically symmetric solutions partially accomplished in a previous paper [Class.Quant.Grav. (2010) 27 205024]. In this approach we consider every compatible algebraic type of the Ricci tensor,…

This article deals with the investigation of perfect fluid spacetimes endowed with concircular vector field. It is shown that in a perfect fluid spacetime with concircular vector field, the velocity vector field annihilates the conformal…

Advances in modern physics since Einstein have made the nonsymmetric metric (0,2)-tensor $G=g+F$, where $g$ is a pseudo-Riemannian metric associated with gravity, and $F\ne0$ is a skew-symmetric tensor associated with electromagnetism, more…

In this paper the application of the $M$-projective curvature tensor in the general theory of relativity has been studied. Firstly, we have proved that an $M$-projectively flat quasi-Einstein spacetime is of a special class with respect to…

We continue our study of the mixed Einstein-Hilbert action as a functional of a pseudo-Riemannian metric and a linear connection. Its geometrical part is the total mixed scalar curvature on a smooth manifold endowed with a distribution or a…

In this paper we study the geometry of $\varphi$-static perfect fluid space-times ($\varphi$-SPFST, for short). In the context of Einstein's General Relativity, they arise from a space-time whose matter content is described by a perfect…

Applying the method of conformal metric to a given static axially symmetric vacuum solution of the Einstein equations, we have shown that there is no solution representing a cosmic ideal fluid which is asymtotically FLRW. Letting the cosmic…

We present a review of the Semi-Symmetric Metric Gravity (SSMG) theory, representing a geometric extension of standard general relativity, based on a connection introduced by Friedmann and Schouten in 1924. The semi-symmetric connection is…

In this paper, the theory of space-time in 4-dimensional Kaehler manifold has been studied. We have discussed the Einstein equation with cosmological constant in perfect fluid Kaehler space-time manifold and proved that the isotropic…

We show that a connection with skew-symmetric torsion satisfying the Einstein metricity condition exists on an almost contact metric manifold exactly when it is D-homothetic to a cosymplectic manifold. In dimension five, we get that the…

The aim of this paper is to examine some obtained exact solutions of the Einstein-Maxwell equations, especially their properties from a chronological point of view. Each our spacetime is stationary cylindrically symmetric and it is filled…